Pathways to the optimal set in linear programming. (English) Zbl 0687.90056

Megiddo, Nimrod

Progress in mathematical programming. Interior-point and related methods, Proc. Conf., Pacific Grove/Calif. 1987, 131-158 (1989).

[For the entire collection see Zbl 0669.00026.]
The author presents continuous paths leading to the set of optimal solutions of a linear programming problem. These paths are derived from the weighted logarithmic barrier function. The author gives properties of the tangents to the paths, some observations on higher-order derivatives associated with the paths and generalizations to the linear complementarity problem.

Reviewer: D.I.Duca

MSC:

90C05	Linear programming
90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Keywords:

continuous paths; weighted logarithmic barrier function; tangents; higher-order derivatives

Citations:

Zbl 0669.00026